The Employment Act in Singapore does not govern on such matters, where no specific period has been mandated by legislation. However, it is mandated that Key Employment Terms (KET) is to be issued within 14 days of Employment. As those terms – Start Date, Salary, Daily Working Hours, etc. – usually form part of the contract, we can take the mandated 14 days period as reference.
Aside, I believe it is a good practice to issue Employment Contract before his / her first date of appointment, to prevent any possible disputes after employment.
Reference can be found under my Page “Sources”:
Starting a Contract of Service